A diesel engine in which an engine exhaust passage is branched to a pair of exhaust branch passages for purifying NO.sub.x in the diesel engine, a switching valve is disposed at the branched portion of these exhaust branch passages, the switching valve is switched each time a predetermined time passes to alternately guide the exhaust gas to one of the exhaust branch passages, and a catalyst which can oxidize and absorb the NO.sub.x is disposed in each of the exhaust branch passages is well known (refer to Japanese Unexamined Patent Publication No. 62-106826). In this diesel engine, the NO.sub.x in the exhaust gas introduced into one exhaust branch passage is oxidized and absorbed by the catalyst disposed in that exhaust branch passage. During this time, the inflow of the exhaust gas to the other exhaust branch passage is stopped and, at the same time, a gaseous reducing agent is fed into this exhaust branch passage. The NO.sub.x accumulated in the catalyst disposed in this exhaust branch passage is reduced by this reducing agent. Subsequently, after the elapse of a predetermined time, the introduction of the exhaust gas to the exhaust branch passage to which the exhaust gas had been introduced heretofore is stopped by the switching function of the switching valve, and the introduction of the exhaust gas to the exhaust branch passage to which the introduction of the exhaust gas had been stopped heretofore is started again. That is, in this diesel engine, seen from the viewpoint of each of the exhaust branch passages, exhaust gas is made to flow for a predetermined time during which the NO.sub.x in the exhaust gas is oxidized and absorbed by the catalyst, then the inflow of exhaust gas is stopped for a predetermined period and a reducing agent is fed, whereby the NO.sub.x accumulated in the catalyst is reduced.
However, the amount of the NO.sub.x which is discharged from the engine changes depending on the operating condition of the engine and therefore the amount of the NO.sub.x which is oxidized and absorbed by the catalyst during the predetermined time when the exhaust gas is flowing changes depending on the operating state of the engine during that period. Accordingly, there is the problem that when an engine operating condition under which a large amount of NO.sub.x is discharged continues, the NO.sub.x oxidizing and absorbing ability of the catalyst ends up becoming saturated during the predetermined time in which the exhaust gas flows and as a result the NO.sub.x can no longer be oxidized and absorbed by the NO.sub.x absorbent, so the NO.sub.x is released into the atmosphere.
As opposed to this, when an engine operating condition in which a small amount of NO.sub.x is discharged continues, only a small amount of NO.sub.x is oxidized and absorbed in the predetermined time in which the exhaust gas flows. Accordingly, in this case, when the inflow of the exhaust gas is stopped and the reducing agent is fed, only part of the reducing agent is used for the reduction of the NO.sub.x and the reducing agent becomes in excess, resulting in the problem of the release of this excess reducing agent into the atmosphere.